Some background.
I was asked to find an arithmetic function $f$ such that $f*f=\mathbf 1$ where $\mathbf 1$ is the constant function 1 and $*$ denotes Dirichlet convolution. I was able to prove that ...

I am trying to find a nice formula for
\begin{align}\sum_{m=0}^n{2m\choose m}{2(n-m)\choose n-m}\tag{1}.\end{align}
After failing to simplify it,
I asked WolframAlpha (see link),
and apparently,
it ...